For plasma dynamics, more encompassing than the magnetohydrodynamical (MHD) approximation, the foundational concepts of "magnetic reconnection" may require deep revisions because, in the larger dynamics, magnetic field is no longer connected to the fluid lines; it is replaced by more general fields (one for each plasma specie) that are weighted combination of the electromagnetic and the thermal-vortical fields. We study the two-fluid plasma dynamics plasma expressed in two different sets of variables: the two-fluid (2F) description in terms of individual fluid velocities, and the one-fluid (1F) variables comprising the plasma bulk motion and plasma current. In the 2F description, a Connection Theorem is readily established; we show that, for each specie, there exists a Generalized (Magnetofluid/Electro-Vortic) field that is frozen-in the fluid and consequently remains, forever, connected to the flow. This field is an expression of the unification of the electromagnetic, and fluid forces (kinematic and thermal) for each specie. Since the magnetic field, by itself, is not connected in the first place, its reconnection is never forbidden and does not require any external agency (like resistivity). In fact, a magnetic field reconnection (local destruction) must be interpreted simply as a consequence of the preservation of the dynamical structure of the unified field. In the 1F plasma description, however, it is shown that there is no exact physically meaningful Connection Theorem; a general and exact field does not exist, which remains connected to the bulk plasma flow. It is also shown that the helicity conservation and the existence of a Connected field follow from the same dynamical structure; the dynamics must be expressible as an ideal Ohm's law with a physical velocity. This new perspective, emerging from the analysis of the post MHD physics, must force us to reexamine the meaning as well as our understanding of magnetic reconnection. © 2018 Author(s).